The earliest Garth parish register entry within 10 miles of Rochdale on LANOPC is marriage banns at St. Mary, Oldham 1790 for Robert Garth and Mary Butterworth, both of the parish. I don't see a marriage for them.
Robert and Nancy Garth, abode Toad Lane, Rochdale, had daughter, Sarah baptised at St. Chad, Rochdale, 12th Nov. 1797 (previous day to John Garth's wedding there).
A Robert & Ann Garth had children baptised at Shaw Chapel, Oldham from 1800. Joseph (1800), Thomas (1805), Samuel (1808). Abode was High Crompton 1800 & 1805 and Pastuers 1808. Robert's occupation was weaver in 1800 and farmer 1808. The 2 occupations are compatible.
Shaw Chapel was C. of E.
A Robert Garth, aged 54 was buried at Shaw Chapel 1823.
There are wills at Lancashire Archives of Robert Garth, farmer, High Crompton , Prestwich-with-Oldham (1823) and of Nancy Garth, widow of same place (1841).
High Crompton is/was on the Rochdale side of Shaw.
There were other Garth couples in High Crompton. John & Mary; James & Fanny; Robert & Sally. Each couple named a son Reuben. John & Mary had 2 Reubens. James and Fanny seemed to switch religious allegiance, unless they were different couples. Son, Livi (Levi?) baptised at Union St. Wesleyan Chapel, Rochdale 1821. Previous children baptised at St. Paul, Royton.